BS Math to PhD Astrophysics, need MS Astrophysics or not?

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I'm currently completing a undergraduate BS Mathematics degree and want to go for a PhD in Astrophysics.
I haven't decided on the precise area or topic yet, since there are so many fascinating areas of research, but I might have narrowed it down by the time I actually need to apply.

A tutor once told me to bypass the master's and go straight into PhD studies, but I think he was assuming I would be sticking to the same field as my undergraduate degree.

Do I need to transition with an MS in Astrophysics for more physics/astrophysics training, or should I apply directly for the PhD if I have already managed to choose a topic?
Which courses should I take in my graduating year to help my chances of successful study in astrophysics (I'm learning Python on the side)?

In my final undergraduate year, I must choose four from:

Complex Analysis,
Fluid Mechanics,
Deterministic & Stochastic Dynamics,
Optimisation,
Graphs and Networks,
Probability,
Statistics,
Quantum Theory,
and Electromagnetism.
 
on Phys.org
How much physics have you studied already?

In the US, students entering a PhD program in physics (which includes the master's level coursework that is normally a separate degree in other countries) are generally expected to have completed at least these core physics courses above the introductory level: classical mechanics, electromagnetism, quantum mechanics, and thermodynamics + statistical mechanics. I would expect this to hold also for astrophysics PhD programs.

The situation may be different in other countries.
 
@jtbell

I have only UK high-school physics plus whichever options I take in the final undergraduate year, most likely quantum theory, electromagnetism, and cosmology (theoretical & observational cosmology, and high energy processes). Classical mechanics will be covered in undergraduate mathematics.

Would it be too much to pick up the rest in the first-year of the PhD?
 
I'd like to post a response with an analogy...

Kid: Dad, I met this girl and I want to get married.

Dad: Interesting. How long have you been dating this girl?

Kid: Well, we haven't really gone on a date yet. But I really like her. I had a class with her in high school though. I have a small opportunity to go on a couple of dates with her. Do you think I should?

Dad: What's her name?

Kid: I'm not really sure. I hope to have that figured out by the time I propose to her though.

Dad: I think you should learn her name first, then ask her out on more than just a few dates before you make any kind of long term commitment.More seriously I'm just trying to say that from my point of view it seems like committing to a PhD without having taken any advanced classes in physics yet might be getting ahead of yourself.
 
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But this girl I just met is really hot and I know she's the one. Yes, I'm already dating a girl similar to her but the thing is, she's is a little too formal at times and not open to experimentation. I think I'm beginning to understand her ways really well, but I feel like we're in a bubble and what I want most is for her to show me the ways of the world and the universe at large.
 
umzung said:
Would it be too much to pick up the rest in the first-year of the PhD?
You should fill in any missing (essential) courses before you try to enter a PhD program. Admissions to PhD programs is competitive. The criteria include (1) courses taken and grades (marks) received; (2) your score in the physics Graduate Record Exam (GRE); (3) previous research experience; (4) letters of recommendation. If you're lacking in one area, you need to have a very strong showing in the other areas in order to be competitive. The exact mix varies from one school to another.

Most schools have many more applications than they have spaces. You should ask yourself, "why should a grad school admit me, over a student who has completed an undergraduate physics degree and done well in it?"

Again, this is for the US system.
 

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